Since there's a walkthrough here, I decided to make an achievement guide instead. I know that the achievements in this game are either self-explanatory or story related, but I decided to list it anyway to make it clearer.

I'll try compiling a list of the threads that help me to finish the game too in case there's someone who needs it later.

You'll get them on story progression.

The Folly of Darius Garcia
Identify The Fixer.


Little Big Pharma
Expose Garymax Pharmaceutical's secrets.


Al-Amuq!
Find Lahinzi Turanur.


Al-Amuq! Part 2
Stop Tareek's plans.


Teacher's Pet
Reverse Debra Nielsen's corrupt actions.


The Naughty Nuke
Stop Commander Ponchik from carrying out his orders.


Gridlock
Help the police capture the disgraced ambassador.


The Perfidious Politician
Ensure Senator O'Connell doesn't get another term.


Holy Holophone!
Steal the tech blueprints.


Air Traffic Chaos
Land the planes safely before time runs out.


Kollusion Kourse
Expose the ridiculous hood-wearing hate clowns.


Criminal Cola
Find out what the secret ingredient in Gessner Kola is.


The Kidnapping of Katie Suzuhara
Help the authorities track the kidnapped girl.


Who's Afraid Of The Big Bad Bioweapon?
Eliminate the Savanide threat.


Hospital Hijinks
Identify the sleeping spy.


Who Killed Cassandra Watkins?
Find Cassie Watkin's killer.


The Dancing Devil
Reveal Dante Dimasalang's nefarious schemes.


Seven
Learn Seven's secret identity.


The Perjurious Policeman
Expose the corrupt cop.


Iliuvatar Descends
Save the crew.


GREYHAT
Complete GREYHAT - A Digital Detective Adventure

I'm in!
Tunnel into another computer for the first time.


Complete tunneling minigame in any difficulty BESIDES Auto. You can change the difficulty by pressing the button in the bottom-left corner.

Math Zombies?!
Play Undead AfterMath


After you finished Al-Amuq! mission, open Internet Browser. Visit "Port Forward - Sharing is Caring" and click the GET button next to "[ASHL] Undead AfterMath v1.0233". Install and run it. You can freely close the game afterward.

Willow Way
Collect all 4 of Willow Way's poems.


The Genie & The Merchant
Collect every chapter of The Genie & The Merchant.


Wallpaper
Collect all wallpapers.


In order to get these achievements, you need to drag yellow files to the yellow box in the bottom-right corner. There is usually one yellow file and 3 CatCoins in every level except for the last one.

Some helpful links to help you finish the game:
Walkthrough
After getting the Image Reconstructor
Air Traffic Control tips

Air Traffic Control no crashing planes video:
https://youtu.be/UVFZOiOrGy8

There are some areas that I couldn't explore in the game so I'll just leave it here. Feel free to let me know if you know the solution.

1. Cold Cases folder password in Barnett's PC (The Kidnapping of Katie Suzuhara or Who Killed Cassandra Watkins? mission) The folder is a red herring (thanks Dooms!)
   
2. How to solve the second level of the exam in The Dancing Devil mission. BatStevo confirmed that it can't be solved
   
3. Emily's B cipher (AMAR ???)

That's all, I think. Let me know if there are more things that I need to link or update and I'll update the guide ASAP. Enjoy the game!

Missing Achievement (I'm in)
How on earth (spoilers)